Algorithmic Developments and Software Engineering for Scalable Sparse Eigensolvers in the DFG Project ESSEX

In the German Research Foundation (DFG) project ESSEX (Equipping Sparse Solvers for Exascale), we develop scalable sparse eigensolver libraries for large quantum physics problems. Partners in ESSEX are the Universities of Erlangen, Greifswald, Wuppertal, Tokyo and Tsukuba as well as DLR. The ESSEX Sparse Solver Repository (ESSR) follows a distributed software development strategy using the distributed version control system Git and supports application driven fault tolerance. ESSR includes the kernel library GHOST (General, Hybrid, and Optimized Sparse Toolkit) and the flexible software framework PHIST for implementing iterative methods on HPC systems. PHIST (Pipelined Hybrid Iterative Solver Toolkit) has been developed containing an interface to the existing numerical software framework Trilinos originally. PHIST also includes adapters to basic building block libraries so that high-level algorithm developments can benefit from high-performance kernel implementations, e.g. sparse matrix-vector multiplication kernels. For solving huge sparse eigenproblems on extreme computing systems, we present our algorithmic approaches regarding Jacobi-Davidson methods with preconditioning, FEAST-like methods and Chebyshev filter diagonalization. The former method is applied to determine extreme eigenvalues and -vectors, while the latter two methods are well suited for solving interior eigenproblems. Moreover, we describe the software architecture of our solver toolkit PHIST